A Variational Bayesian-Based Correntropy Cubature Kalman Filter for Drug Release Estimation Using a Second-Order Model

Abstract

Ultrasound-triggered liposomes designed for specific targeting show promise as a drug delivery system, with the potential to enhance the effectiveness of chemotherapy while minimizing related side effects in clinical settings. This paper aims to model the drug release rate of seven targeted liposomes using a second-order discrete equation rather than the previously used first-order equation. By modeling the rate as second-order, different variants of the Kalman Filter can be applied to estimate the drug release rate. After modeling the equations and fitting the data to a second-order model, the Kalman filter variants, including the Extended Kalman Filter (EKF), Cubature Kalman Filter (CKF), and the Variational Bayesian-Based Correntropy Cubature Kalman Filter (VBMCCKF), were used to estimate the drug release rate. By applying those variants, we can see that the VBMCCKF yields the best tracking performance, combining the Variational Bayesian KF (VBKF’s) adaptive estimation of measurement noise with the MCCKF’s setting of the filter gain to a very small value when an abnormal measurement is detected. As a result, the VBMCCKF yielded the lowest Mean Squared Error (MSE) and Root Mean Squared Error (RMSE).